Models, Prediction & Forecasting

A model is a description of a system or process to show how it works.

Physical models are used in many ways. Architects use them to enable clients to visualise proposed buildings and how they might be used. Engineers use them to develop and test ideas. Scientists use them to investigate new molecules. Children use dolls and toys to explore possible social and material worlds.

We have mental models about all aspects of our lives and we use them to try to understand things and decide what to do. Soap operas provide models of social interaction while history and myths provide models of heroism and human frailty. Implicitly or explicitly we form models of our friends and workmates and use these models to guide what we do. Many models support reasoning and allow deductions to be made about future actions and their likely outcomes. For the most part they are heuristic – rules of thumb that usually work but sometimes don’t.

Scientists construct formal models of systems, often using mathematics. The gold standard for conventional science is prediction. To be accepted a model has to predict future events and those events have to be verified empirically by experiment. If any observation is inconsistent with the theory, then the theory is partially or totally wrong. In this respect all scientific knowledge is contingent. Physics has had great success as a science correctly predicting events such as the appearance of Halley’s Comet over hundreds of years.

The conventional scientific approach is a not applicable for complex systems such as the spread of disease in the modern world. Even if we had a perfect model for a lethal viral pandemic it would not be ethically acceptable to run experiments to verify it. Another more practical reason is that many systems are sensitive to initial conditions. This means that if it were possible to re-run a system from the ‘same’ starting position its trajectory would diverge over time to make its position increasingly unpredictable. For any real system measuring the ‘same’ initial position involves error, no matter how small. Even the tiniest errors can get amplified to become very large.

Sensitivity to initial conditions

Systems that are sensitive to initial conditions and bounded are said to be chaotic. This is a technical term and is not to be taken literally. The weather is a classic example of a chaotic system. Although the weather is unpredictable from the conventional scientific perspective, it is possible to forecast it. For example, the weather forecast for my city in two hours is that it will be cloudy with a 10% chance of rain [it was cloudy with no rain], and at the same time tomorrow it will be sunny with a 3% chance of rain [there was weak evening sunshine].

Most social systems are sensitive to initial conditions. For example, if that farmer had not gone to that market in Wuhan on that day there might not have been the coronavirus pandemic. If that person had not caught a plane to Italy the disease might have been appeared some days or weeks later and its effects been less severe. If a different president had been in the White House the progress of the epidemic in the USA might have been different.

When a system is sensitive to initial conditions a single calculation or run tells you very little. However when the model is run many times with many sets of initial conditions a view can be obtained of the ‘space’ of possible futures. Sometimes simulations produce results that no-one expected giving insights into the ‘unknown unknowns’.

Prediction Exercise

Figure 13.1. New cases Covid-19 in the UK to 13^thApril 2020

Figure 13.1 shows the number of new cases of Covid-19 in the UK to 13^th April 2020. On the 12^th April it was 5288 and on the 13th April it was 4342. What do you think the number of new cases was on 14^th April? It is one of the numbers below

Make a note of your prediction so that you can enter it in the next step.

Summary

The main points of this step are:

• a model is a description of a system or process to show how it works

• prediction is the gold standard for conventional science

• point prediction is usually not possible in complex systems

• sensitivity to initial conditions precludes point prediction

• models and computer simulation allows the future to be explored

• modelling can expose unknown unknowns

• future system states can be forecast within confidence limits

• modelling is imperfect but the best we have for forecasting

What do you think?

Do you think models can give useful forecasts? Do you have models of things expressed in words? Do you trust computer simulations?